Quadrilateral OPQR is inscribed in circle N, as shown below. Which of the following could be used to calculate the measure of ∠PQR? (6 points) Circle N is shown with a quadrilateral OPQR inscribed inside it. Angle O is labeled x plus 16. Angle P is not labeled. Angle Q Select one: a. (6x − 4)° + (2x + 16)° = 180° b. (x + 16)° + (6x − 4)° = 180° c. (6x − 4)° + (2x + 16)° = 360° d. (x + 16)° + (6x − 4)° = 360°

b. (x + 16)° + (6x − 4)° = 180°

Step-by-step explanation:

As we know that in a quadilateral the total of the opposite angles in a circle is equivalent to the 180 degrees

As seen in the attached figure

∠ROP + ∠RQP = 180 degrees

So

(x + 16)° + (6x - 4)° = 180 degrees

Hence, the correct option is b.

Therefore all the other options which are given is incorrect

I believe the answer is

A. Vertical angles prove Angle1 Is congruent to Angle4.

C. Angle5 and Angle3 are alternate interior angles

E. The triangles are similar because all corresponding angles are congruent.